Auto-Math
Sans calculatrice, calculez \(\sin\theta\) si \(\theta=315^{\circ}\).
\( -\dfrac{1}{2} \)
\( -\dfrac{\sqrt{2}}{2} \)
\( \dfrac{\sqrt{2}}{2} \)
\( \dfrac{7\pi}{4} \)
Déterminez à l'aide du cercle trigonométrique la valeur de \( \sin\dfrac{3\pi}{4} \).
\( \dfrac{1}{2} \)
Résolvez l'équation \(\sin x = \dfrac{\sqrt{2}}{2} \).
\( S=\left\{\dfrac{\pi}{4}\right\} \)
\( S=\left\{\dfrac{\pi}{4},\, \dfrac{3\pi}{4}\right\} \)
\( S=\left\{\dfrac{\pi}{4}+2k\pi,\, \dfrac{3\pi}{4}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{4}+2k\pi,\, \dfrac{7\pi}{4}+2k\pi;\, k\in\mathbb{Z}\right\} \)
Sachant que \(ABCD\) est un carré inscrit dans un cercle de centre \(O \), comparez les angles \(\widehat{CAD}\) et \(\widehat{CBD}\) .
\( \widehat{CAD}=\widehat{CBD} \)
\( 2\widehat{CAD}=\widehat{CBD} \)
\( \widehat{CAD}=2\widehat{CBD} \)
\( \widehat{CAD}=\dfrac{1}{2}\widehat{CBD} \)
Convertissez en radians l'angle \(-135^\circ \).
\( -135\mbox{ radians}\)
\( \dfrac{3\pi}{4}\mbox{ radians}\)
\( \dfrac{5\pi}{4} \mbox{ radians}\)
\( -\dfrac{5\pi}{4} \mbox{ radians}\)
Résolvez l'équation \(2\sin{3x}+\sqrt{2}=0\) .
\( S=\left\{\dfrac{5\pi}{12},\, \dfrac{7\pi}{12}\right\} \)
\( S=\left\{\dfrac{5\pi}{12}+2k\dfrac{\pi}{3},\, \dfrac{7\pi}{12}+2k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
\(S=\left\{\dfrac{5\pi}{12}+2k\pi,\, \dfrac{7\pi}{12}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{7\pi}{12}+2k\dfrac{\pi}{3};\, k\in\mathbb{Z}\right\} \)
Convertissez en radians l'angle \(390^\circ \).
\(30\mbox{ radians}\)
\(\dfrac{\pi}{3} \mbox{ radians}\)
\( \dfrac{\pi}{6}\mbox{ radians}\)
\( 2\pi \mbox{ radians}\)
Sachant que \(ABCD\) est un carré inscrit dans un cercle de centre \(O \), comparez les angles \(\widehat{COD}\) et \(\widehat{CAD} \).
\( 2\widehat{COD}=\widehat{CAD} \)
\( \widehat{COD}=2\widehat{CAD} \)
\( \widehat{COD}=\widehat{CAD} \)
\( \widehat{COD}=\dfrac{1}{2}\widehat{CAD} \)
Résolvez l'équation \( \cos x = -{1\over 2} \).
\( S=\left\{\dfrac{2\pi}{3}\right\} \)
\( S=\left\{\dfrac{2\pi}{3},\, \dfrac{4\pi}{3}\right\} \)
\( S=\left\{\dfrac{2\pi}{3}+2k\pi,\, \dfrac{4\pi}{3}+2k\pi;\, k\in\mathbb{Z}\right\} \)
\( S=\left\{\dfrac{\pi}{3}+2k\pi,\, -\dfrac{\pi}{3}+2k\pi;\, k\in\mathbb{Z}\right\} \)
Donnez la valeur de \( \sin {\pi \over 2}\) .
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